CN114840802B - A method for identifying the natural evolution type of hydroclimatic processes - Google Patents

Abstract

The invention discloses a method for distinguishing the natural evolution type of a hydrologic climate process, which comprises the following steps: solving the time sequences of the five natural evolution types, performing differential processing, and estimating the corresponding first-order autocorrelation coefficients and second-order autocorrelation coefficients by a Monte Carlo test to obtain the corresponding 95% confidence intervals; identifying a mutation component in a time sequence to be analyzed, removing the mutation component and the seasonal component of the time sequence, and taking the rest component as a new time sequence; after the difference processing is carried out on the new time sequence, the first-order autocorrelation coefficient and the second-order autocorrelation coefficient of the new time sequence are solved, and compared with 95% confidence intervals corresponding to the various types, the specific natural evolution type of the time sequence to be analyzed is determined. The invention utilizes Monte Carlo test to determine the confidence interval of various natural evolution type statistical characteristics, and accurately distinguishes white noise, unit root process, AR (1) process and AR (2) process based on the confidence interval, thereby avoiding that the AR (1) process and the AR (2) process are misjudged as the error result of long-lasting process.

Description

A method for identifying the natural evolution type of hydroclimatic processes

Technical Field

The present invention belongs to the field of hydrological and climatic science and technology, and specifically refers to a method for determining the natural evolution type of hydrological and climatic processes.

Background technique

Accurately revealing the evolution characteristics of hydrological and climatic processes and understanding their future evolution is the basic basis and necessary prerequisite for scientifically assessing climate change and rationally responding to the impact of climate change. Affected by the combined effects of multiple complex factors (including random factors), the actual hydrological and climatic process is very complex, especially in recent decades, under the increasing impact of global change, the hydrological and climatic process has become more complex and changeable.

At present, the research on the evolution characteristics of hydrological and climatic processes mainly focuses on trends and natural evolution characteristics, among which the natural evolution characteristics mainly focus on short-duration characteristics and long-duration characteristics. When the autocorrelation function C(s) decays rapidly to 0 or decays in an exponential function as the time interval increases, the sequence presents a short-duration characteristic; on the contrary, when the autocorrelation function C(s) decays very slowly or decays in the form of a power function, the sequence presents a long-duration characteristic. The research on short-duration characteristics started earlier, and researchers have successively proposed AR models, MA models, and ARMA models to describe the short-duration characteristics of time series. Hurst analyzed the long-term observation data of the Nile River and found that the autocorrelation function of the sequence showed a slow decay state. This phenomenon was later called the "Hurst phenomenon". Since the values of the sequence with the "Hurst phenomenon" are still connected over a long period of time, it is also called a long-duration characteristic, a long-correlation characteristic, or a long-distance dependence characteristic, and the parameter d represents the size of the long-duration characteristic of the sequence. When d>0, the sequence presents a long-duration characteristic; when d<0, the sequence presents an anti-duration characteristic; when d＝0, the sequence presents a short-duration characteristic or there is no correlation. In particular, when d = 1, the time series is transformed into a unit root process, which not only produces an obvious random trend, but also a "pseudo-regression" phenomenon occurs between time series. Therefore, identifying and distinguishing different natural evolution types of hydrological and climatic processes is an important prerequisite for accurately revealing the evolution characteristics of hydrological and climatic processes, scientifically assessing climate change, and rationally responding to the impact of climate change.

At present, the study of the natural evolution characteristics of hydroclimatic processes is mainly based on the long-persistence characteristics evaluation method. The long-persistence characteristics evaluation methods are mainly divided into three categories: non-parametric estimation method, parameter estimation method and semi-parametric estimation method; non-parametric estimation methods mainly include autocorrelation coefficient analysis method, R/S method, rescaled variance method, detrended fluctuation analysis (DFA), etc.; parameter estimation methods mainly include mean model, volatility model, periodogram method, power spectrum density method and wavelet analysis method; semi-parametric methods mainly include GPH method, local Whittle (Local Whittle, LW) method, and correction methods based on GPH estimator and LW estimator. However, the above long-persistence characteristics evaluation methods are based on the basic premise and assumption that hydroclimatic processes have long-persistence characteristics, but ignore whether this assumption is actually established in practice. Existing studies have shown that the long-persistence characteristics evaluation method is prone to misdetecting short-persistence characteristics as long-persistence characteristics, and as the data sample size increases, the d value of the AR(1) process gradually tends to 0, at which time it can be accurately detected that the AR(1) process does not belong to the long-persistence characteristics. However, due to the limitation of the length of observation data, it is impossible to accurately evaluate and distinguish long-duration characteristics from short-duration characteristics. Therefore, tree ring and other proxy data are used in the study of long-duration characteristics. Studies have shown that proxy data will underestimate long-duration characteristics, while low-resolution proxy data will overestimate long-duration characteristics, that is, proxy data cannot be used to distinguish short-duration characteristics from long-duration characteristics of hydrological and climatic processes. There are often noise, trend and other components in actual time series, which leads to deviations or errors in the results of most long-duration characteristics estimation methods. Compared with the above-mentioned long-duration characteristics evaluation methods, the DFA method can effectively filter out the trend components of various orders in the time series, and is suitable for the analysis of long-duration characteristics of non-stationary time series. Its principle is to eliminate the trend components generated by external factors in the time series, and then estimate the long-duration characteristics of the remaining components. Therefore, it is widely used in the study of long-duration characteristics of hydrological and climatic processes.

In recent years, some scholars have proposed that the DFA method can be used to accurately distinguish between AR(1) processes and long-duration processes. The AR(1) process has d>0 on the entire time scale and d=0 on the large time scale, while the long-duration characteristics of the long-duration process are both d>0 on the entire time scale and the large time scale. Based on this, the DFA method can avoid the AR(1) process being misjudged as the result of the long-duration process. However, this method is only applicable to the AR(1) process. It is difficult to accurately describe the actual observed time series using the AR(1) process, and higher-order autocorrelation characteristics need to be considered. However, for higher-order AR(p) (p>1) processes, the DFA method still cannot accurately distinguish between short-duration processes and long-duration processes. Usually, the autocorrelation function is used to determine the order of the AR process, but due to the influence of the determined components, the autocorrelation coefficient has a large deviation.

Summary of the invention

In view of the above-mentioned deficiencies in the prior art, the purpose of the present invention is to provide a method for distinguishing the natural evolution types of hydrological and climatic processes, so as to solve the defect that the prior art ignores the applicability of long-duration characteristic evaluation methods, resulting in the inability to accurately distinguish and differentiate different natural evolution types of hydrological and climatic processes.

To achieve the above object, the technical solution adopted by the present invention is as follows:

A method for distinguishing the natural evolution type of hydroclimatic process of the present invention comprises the following steps:

1) Generate five types of time series with the same length as the time series TS(t) to be analyzed: white noise, AR(1) process, AR(2) process, unit root process, and long-duration process. Perform difference processing on each generated time series and solve the corresponding first-order autocorrelation coefficient and second-order autocorrelation coefficient;

2) Repeat the above step 1) until the statistical characteristics of the first-order autocorrelation coefficient and the second-order autocorrelation coefficient of each type of time series after difference processing tend to be stable, and then obtain the 95% confidence interval corresponding to the first-order autocorrelation coefficient and the second-order autocorrelation coefficient of each type of time series after difference processing;

3) Identify the mutation component B ₀ in the time series TS(t), solve the multi-year average seasonal component S ₀ , remove the mutation component B ₀ and seasonal component S ₀ of the time series TS(t), and use the remaining components as the new time series TS'(t)=TS(t)-B ₀ -S ₀ ;

4) After performing difference processing on the new time series TS’(t), solve its first-order autocorrelation coefficient AC_diff(1) and second-order autocorrelation coefficient AC_diff(2);

5) Compare the first-order autocorrelation coefficient AC_diff(1) and the second-order autocorrelation coefficient AC_diff(2) with the 95% confidence intervals of the first-order autocorrelation coefficient and the second-order autocorrelation coefficient after time series difference processing of white noise, AR(1) process, AR(2) process, unit root process, and long-duration process obtained in step 2) to determine the specific natural evolution type of the time series TS(t).

Furthermore, the step 1) specifically includes:

11) Generate a white noise time series y ₁ (t) using the Monte Carlo method;

12) The time series y ₂ (t) of the AR(1) process is generated using the first-order autoregressive model as follows:

y ₂ (t) = ρ × y ₂ (t-1) + u (t)

Where t represents the time series; ρ is the first-order autocorrelation coefficient, and |ρ|<1, u(t) is a white noise sequence with a mean of 0 and an independent and identical distribution;

13) The time series y ₃ (t) of the AR(2) process is generated using the second-order autoregressive model as follows:

y ₃ (t) = ρ ₁ × y ₃ (t-1) + ρ ₂ × y ₃ (t-2) + u(t)

Where ρ ₁ and ρ ₂ are the first-order and second-order autocorrelation coefficients, ρ ₁ +ρ ₂ <1, ρ ₂ -ρ ₁ <1, -1<ρ ₂ <1;

14) Generate the time series y ₄ (t) of the unit root process as follows:

y ₄ (t) = y ₄ (t-1) + u (t)

15) Use the ARFIMA model to generate the time series y ₅ (t) of the long-lasting process.

Furthermore, the step 5) specifically includes:

51) When AC_diff(1) and AC_diff(2) are within the 95% confidence interval of white noise, the natural evolution type of the time series TS(t) is determined to be a white noise process;

52) When AC_diff(1) and AC_diff(2) are within the 95% confidence interval of the unit root process, the natural evolution type of the time series TS(t) is determined to be a unit root process;

53) When AC_diff(1) and AC_diff(2) are within the 95% confidence interval of the AR(2) process, the natural evolution type of the time series TS(t) is determined to be an AR(2) process;

54) If AC_diff(1) and AC_diff(2) are within the 95% confidence interval of the long-lasting process or the AR(1) process, the DFA method is used to solve the scaling exponent α of the new time series TS’(t) to further identify the natural evolution type of TS(t).

Furthermore, the step 54) specifically includes:

541) Use the DFA method to obtain the fluctuation function F(s) of the new time series TS’(t) and the double logarithmic scatter plot (ln(F(s)), ln(s)) of the time scale s;

542) identifying the structural mutation point B ₁ of the double logarithmic scatter plot;

543) The least square method is used to perform linear fitting on ln(F(s)) and ln(s) in the interval B ₁ <s<L/4, where the linear trend is the scaling index α and L is the sequence length of the time series TS(t);

544) If α = 0.5, the natural evolution type of the time series TS(t) is determined to be an AR(1) process;

545) If α>0.5, the natural evolution type of the time series TS(t) is determined to be a long-duration process.

Beneficial effects of the present invention:

The present invention uses Monte Carlo experiments to determine the confidence intervals of the statistical characteristics of various natural evolution types, and uses this as a basis to accurately distinguish white noise, unit root processes, and AR (2) processes, thereby avoiding the erroneous result that the AR (2) process is misjudged as a long-lasting process;

The present invention uses the DFA method to further distinguish between AR(1) processes and long-duration processes, avoiding the erroneous operation of directly using the LocalWhittle method to misjudge the AR(1) process as a long-duration process, thereby accurately identifying and distinguishing the five main types of natural evolution of hydroclimatic processes. The results are more reasonable and reliable than those of conventional methods, and can provide a scientific basis for scientifically evaluating climate change and rationally responding to the impacts of climate change.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 is a flow chart of the method of the present invention;

FIG2 a is a schematic diagram of an artificially generated sequence S11 of the AR(2) process;

FIG2 b is a schematic diagram of the artificially generated sequence S12 of the AR(2) process;

FIG2 c is a schematic diagram of the artificially generated sequence S13 of the AR(2) process;

FIG2 d is a schematic diagram of the artificially generated sequence S14 of the AR(2) process;

FIG3 a is a schematic diagram of an artificially generated sequence S21 of the AR(1) process;

FIG3 b is a schematic diagram of an artificially generated sequence S22 of the AR(1) process;

FIG3 c is a schematic diagram of an artificially generated sequence S23 of a long-lasting process;

FIG. 3 d is a schematic diagram of an artificially generated sequence S24 of a long-lasting process.

Detailed ways

In order to facilitate the understanding of those skilled in the art, the present invention is further described below in conjunction with embodiments and drawings. The contents mentioned in the implementation modes are not intended to limit the present invention.

1, a method for distinguishing the natural evolution type of hydroclimatic process of the present invention comprises the following steps:

1) Randomly set the values of each parameter to generate five types of time series with the same length as the time series TS(t) to be analyzed, namely white noise, AR(1) process, AR(2) process, unit root process, and long-duration process. Perform difference processing on the generated time series to eliminate the influence of random trends, and then solve the first-order autocorrelation coefficient and second-order autocorrelation coefficient of each time series after difference processing;

Wherein, the step 1) specifically includes:

11) Generate a white noise time series y ₁ (t) using the Monte Carlo method;

12) The time series y ₂ (t) of the AR(1) process is generated using the first-order autoregressive model as follows:

y ₂ (t) = ρ × y ₂ (t-1) + u (t)

Where t represents the time series; ρ is the first-order autocorrelation coefficient, and |ρ|<1, u(t) is a white noise sequence with a mean of 0 and an independent and identical distribution;

13) The time series y ₃ (t) of the AR(2) process is generated using the second-order autoregressive model as follows:

y ₃ (t) = ρ ₁ × y ₃ (t-1) + ρ ₂ × y ₃ (t-2) + u(t)

Where ρ ₁ and ρ ₂ are the first-order and second-order autocorrelation coefficients, ρ ₁ +ρ ₂ <1, ρ ₂ -ρ ₁ <1, -1<ρ ₂ <1;

14) Generate the time series y ₄ (t) of the unit root process as follows:

y ₄ (t) = y ₄ (t-1) + u (t)

15) Use the ARFIMA model to generate the time series y ₅ (t) of the long-lasting process.

2) Setting different values for each parameter, repeating the above step 1) to generate different time series of different types, and conducting Monte-Carlo tests until the statistical characteristics (mean and standard deviation) of the first-order autocorrelation coefficient and the second-order autocorrelation coefficient of each type of time series after difference processing tend to be stable;

3) Obtain the mean ±2 times standard deviation interval of the first-order autocorrelation coefficient and the second-order autocorrelation coefficient of each type of time series after difference processing as its corresponding 95% confidence interval, so as to accurately quantify and distinguish the differences between the five types of natural evolution (white noise, AR(1) process, AR(2) process, unit root process, and long-duration process);

4) The Mann-Kendall test method is used to identify the mutation component B ₀ in the time series TS(t), and the multi-year average seasonal component S ₀ is solved. The mutation component B ₀ and the seasonal component S ₀ of the time series TS(t) are eliminated to eliminate the interference and influence of the two on the discrimination of natural evolution types, and the remaining components are used as the new time series TS'(t)=TS(t)-B ₀ -S ₀ ;

5) After performing difference processing on the new time series TS’(t), solve its first-order autocorrelation coefficient AC_diff(1) and second-order autocorrelation coefficient AC_diff(2);

6) Compare AC_diff(1) and AC_diff(2) with the first-order autocorrelation coefficient and the 95% confidence interval of the second-order autocorrelation coefficient of the time series difference processing of white noise, AR(1) process, AR(2) process, unit root process, and long-duration process obtained in step 3) to determine the specific natural evolution type of the time series TS(t); specifically, including:

61) When AC_diff(1) and AC_diff(2) are within the 95% confidence interval of white noise, the natural evolution type of the time series TS(t) is determined to be a white noise process;

62) When AC_diff(1) and AC_diff(2) are within the 95% confidence interval of the unit root process, the natural evolution type of the time series TS(t) is determined to be a unit root process;

63) When AC_diff(1) and AC_diff(2) are within the 95% confidence interval of the AR(2) process, the natural evolution type of the time series TS(t) is determined to be an AR(2) process;

64) When AC_diff(1) and AC_diff(2) are within the 95% confidence interval of the long-duration process or the AR(1) process, the DFA method is used to solve the scaling exponent α of the new time series TS’(t) to further identify the natural evolution type of TS(t).

Preferably, the step 64) specifically includes:

641) Use the DFA method to obtain the fluctuation function F(s) of the new time series TS’(t) and the double logarithmic scatter plot (ln(F(s)), ln(s)) of the time scale s;

642) identifying the structural mutation point B ₁ of the double logarithmic scatter plot;

643) The least square method is used to perform linear fitting on ln(F(s)) and ln(s) in the interval B ₁ <s<L/4, where the linear trend is the scaling index α and L is the sequence length of the time series TS(t);

644) If α = 0.5, the natural evolution type of the time series TS(t) is determined to be an AR(1) process;

645) If α>0.5, the natural evolution type of the time series TS(t) is determined to be a long-duration process.

Example:

Since the natural evolution type of artificially generated sequences is known, the use of artificially generated sequences is conducive to verifying the effectiveness of the method of the present invention. However, the natural evolution type of measured hydrological time series is often unknown, and it is impossible to accurately judge the accuracy of the results of the method of the present invention in distinguishing the natural evolution type of hydrological and climatic processes. In order to prove the accuracy of the results of the method of the present invention in distinguishing the natural evolution type of time series, two types of artificial sequences were generated when the scheme was designed, which were used to verify the effectiveness of the method of the present invention in distinguishing AR (2) processes from long-lasting processes, and distinguishing AR (1) processes from long-lasting processes. The natural evolution characteristics of the first type of time series are AR (2) processes, with the same sequence length, but different autoregressive coefficients of the time series, which are recorded as S11, S12, S13 and S14 (Figure 2a, Figure 2b, Figure 2c, Figure 2d). The second type of sequences have the same sequence length, but different natural evolution types, among which S21 and S22 are AR (1) processes (Figure 3a, Figure 3b), and S23 and S24 are long-lasting processes (Figure 3c, Figure 3d). Different methods are used to determine the natural evolution types of the artificially generated time series. The determination results of the two types of time series are shown in Table 1 and Table 2 (the determination results of the natural evolution types of artificially generated sequences by different methods):

Table 1

Table 2

The natural evolution type discrimination results show that the DFA method cannot accurately identify the AR(2) process, resulting in misjudgment of the natural evolution type of the time series, while the present invention can accurately distinguish between the AR(2) process and the long-duration process. The Local Whittle method cannot accurately distinguish between the AR(1) process and the long-duration process. Compared with the Local Whittle method that directly evaluates the long-duration characteristics of the time series, the method of the present invention first performs differential processing on the time series and uses the first-order and second-order autocorrelation coefficients of the differential time series to identify the AR(2) process, which can overcome the limitations of the DFA method and avoid the AR(2) process being misjudged as a long-duration process; secondly, the DFA method is used to distinguish between the AR(1) process and the long-duration process, further overcoming the misjudgment of the natural evolution type results of the time series due to ignoring the limitations of the Local Whittle method, and finally obtaining accurate natural evolution type results of the time series.

By comparing the above time series natural evolution type identification results, we can draw the following important conclusions:

(1) The DFA method can identify AR(1) processes and long-lasting processes, but cannot accurately distinguish AR(2) processes from long-lasting processes;

(2) Compared with the DFA method, the Local Whittle method is based on the basic assumption that time series have long-lasting characteristics, which will misjudge the AR(1) process as a long-lasting process;

(3) The method of the present invention first identifies the AR(2) process, thus avoiding the misjudgment of the AR(2) process as a long-duration process. Then, the DFA method is used to further distinguish the AR(1) process from the long-duration process, thus overcoming the limitations of other conventional methods. Therefore, the determination results of the natural evolution type of the time series are more reasonable and reliable, which can provide a scientific basis for revealing the evolution characteristics of hydrological and climate processes and scientifically evaluating climate change.

The present invention has many specific application paths. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principle of the present invention. These improvements should also be regarded as the protection scope of the present invention.

Claims (2)

1. A method for distinguishing the natural evolution type of a hydrologic climate process is characterized by comprising the following steps:

1) Respectively generating five types of time sequences of white noise, AR (1) process, AR (2) process, unit root process and long-duration process which are the same as the length of the time sequence TS (t) to be analyzed, carrying out differential processing on each generated time sequence, and then solving the corresponding first-order autocorrelation coefficient and second-order autocorrelation coefficient;

2) Repeating the step 1) until the statistical characteristics of the first-order autocorrelation coefficients and the second-order autocorrelation coefficients after the time series differential processing of each type tend to be stable, and further obtaining 95% confidence intervals corresponding to the first-order autocorrelation coefficients and the second-order autocorrelation coefficients after the time series differential processing of each type;

3) Identifying a mutation component B ₀ in the time sequence TS (t), solving a season component S ₀ which is averaged for a plurality of years, eliminating a mutation component B ₀ and a season component S ₀ of the time sequence TS (t), and taking the rest components as a new time sequence TS' (t) =TS (t) -B ₀-S₀;

4) After differential processing is carried out on the new time sequence TS '(t), a first-order autocorrelation coefficient AC_diff (1) and a second-order autocorrelation coefficient AC_diff (2) of the new time sequence TS' (t) are solved;

5) Comparing the first-order autocorrelation coefficients AC_diff (1) and the second-order autocorrelation coefficients AC_diff (2) with 95% confidence intervals corresponding to the first-order autocorrelation coefficients and the second-order autocorrelation coefficients obtained in the step 2) after the time series difference processing of the various types to determine the specific natural evolution type of the time series TS (t);

The step 5) specifically comprises the following steps:

51 When ac_diff (1) and ac_diff (2) belong to the 95% confidence interval of white noise, then the natural evolution type of the time series TS (t) is determined as white noise process;

52 When ac_diff (1) and ac_diff (2) belong to 95% confidence intervals of the unit root process, then the natural evolution type of the time series TS (t) is determined as the unit root process;

53 When ac_diff (1) and ac_diff (2) belong to the AR (2) procedure within the 95% confidence interval, then the natural evolution type of the time series TS (t) is determined as AR (2) procedure;

54 If the AC_diff (1) and the AC_diff (2) belong to a 95% confidence interval of a long-duration process or an AR (1) process, solving a scale index alpha of a new time sequence TS' (t) by using a DFA method, and further judging the natural evolution type of the TS (t);

The step 54) specifically includes:

541 Obtaining a fluctuation function F(s) of a new time sequence TS' (t) and a double-logarithmic scatter diagram (ln (F (s)), ln (s)) of a time scale s by using a DFA method;

542 Identifying a structural mutation point B ₁ of the double pair number scatter plot;

543 Linear fitting of the intervals B ₁ < s < L/4 ln (F (s)) and ln(s) by means of the least square method, the linear trend being the scale index α, L being the sequence length of the time sequence TS (t);

544 If α=0.5, then the natural evolution type of the time series TS (t) is determined as AR (1) procedure;

545 If α >0.5, the natural evolution type of the time series TS (t) is determined to be a long duration.

2. The method for distinguishing a natural evolution type of a hydrographic climate process according to claim 1, wherein the step 1) specifically comprises:

11 Generating a time sequence y ₁ (t) of white noise using a monte carlo method;

12 A time series y ₂ (t) of the AR (1) generation process using the first-order autoregressive model is as follows:

y₂(t)＝ρ×y₂(t-1)+u(t)

Wherein t represents a time sequence; ρ is a first-order autocorrelation coefficient, and |ρ| <1, u (t) is a white noise sequence with an average value of 0, which accords with independent same distribution;

13 A time series y ₃ (t) of the AR (2) generation process using the second-order autoregressive model is as follows:

y₃(t)＝ρ₁×y₃(t-1)+ρ₂×y₃(t-2)+u(t)

Wherein ρ ₁ and ρ ₂ are the first-order and second-order autocorrelation coefficients, respectively, ρ ₁+ρ₂<1,ρ₂-ρ₁<1,-1<ρ₂ <1;

14 A time series y ₄ (t) of the generation unit root process is as follows:

y₄(t)＝y₄(t-1)+u(t)

15 A time series y ₅ (t) of long duration is generated using ARFIMA models.